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Bifurcation analysis of an orientational aggregation model

Title data

Geigant, Edith ; Stoll, Michael:
Bifurcation analysis of an orientational aggregation model.
In: Journal of Mathematical Biology. Vol. 46 (June 2003) Issue 6 . - pp. 537-563.
ISSN 0303-6812
DOI: https://doi.org/10.1007/s00285-002-0187-1

Project information

Project financing: E.G. is supported by the Sonderforschungsbereich 256 ‘Nonlinear partial differential equations’ (University of Bonn, Germany).

Abstract in another language

We consider an integro-differential equation for the evolution of a function f on the circle, describing an orientational aggregation process. In the first part we analyze generic bifurcations of steady-state solutions when a single eigenvalue changes sign. Lyapunov-Schmidt reduction leads to the bifurcation equation which is solved explicitly by formal power series. We prove that these series have positive radius of convergence. Two examples
exhibit forward and backward bifurcations, respectively. In the second part we assume that the first and second eigenvalues become positive. Again we use Lyapunov-Schmidt reduction to arrive at the reduced bifurcation system from which we get the bifurcating branches as power series. We calculate the two most important parameters of the reduced system for two examples; one of them has interesting mode interactions which lead to various kinds of time-periodic solutions.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Actin; Cytoskeleton; Orientational Aggregation; Bifurcation Analysis; Mode Interaction; Power Series Expansion
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 03 Feb 2015 07:26
Last Modified: 12 Feb 2015 12:19
URI: https://eref.uni-bayreuth.de/id/eprint/6225